Implement a Min-Heap with Insert and Remove-Min

Problem Statement

Implement a binary min-heap from scratch without using any built-in priority queue or heap libraries (such as Python's heapq). Your min-heap must store elements in a contiguous zero-indexed dynamic array and maintain the standard min-heap property: the value of each node must be less than or equal to the values of its children.

Implement the MinHeap class with the following methods:

• __init__(): Initializes an empty min-heap.
• insert(val: int) -> None: Adds an integer val into the heap.
• extract_min() -> int | None: Removes and returns the smallest integer in the heap. If the heap is empty, returns None.
• peek() -> int | None: Returns the smallest integer without removing it. If the heap is empty, returns None.
• size() -> int: Returns the total number of elements currently stored in the heap.

Array Indexing Rules (0-indexed)

For an element at index i:

• Parent: (i - 1) // 2 (for i > 0)
• Left Child: 2 * i + 1
• Right Child: 2 * i + 2

Example

heap = MinHeap()
heap.insert(5)
heap.insert(3)
heap.insert(8)
heap.insert(1)

heap.peek()        # returns 1
heap.extract_min() # returns 1
heap.extract_min() # returns 3
heap.size()        # returns 2
heap.insert(-2)
heap.extract_min() # returns -2
heap.extract_min() # returns 5
heap.extract_min() # returns 8
heap.extract_min() # returns None (heap is empty)

Constraints

• Values inserted can be negative, zero, or positive: -10^9 <= val <= 10^9
• Values may contain duplicates.
• Up to 500,000 total calls across all methods.
• insert and extract_min must run in O(log n) time.
• peek and size must run in O(1) time.
• Auxiliary space (excluding the array storing elements) must be O(1).

Edge Cases

• Calling extract_min() or peek() on an empty heap should safely return None without raising an exception.
• Removing elements until the heap transitions from size 1 to size 0.
• Correctly comparing two children during sift-down when only the left child exists, or when child values are identical.